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BOOK THREE OF MANAGEMENT

Color measurement – the CIE Chapter 9 Color measurement – the CIE 1931 system

Introduction The measurement of a color is basically nothing other than standardised , where the two factors, and observer are standardised. The scientific foundation for color measurement is based on the existence of 3 different groups of signals ( stimuli , and ) that are passed on from the eye of the observer. The starting point for transfer into a standardised system is the sensitivity of the S, M and L cones. Today, the sensitivities, related to the wavelength, are known. As a basis for an international colorimetric system, the International Commission on Illumination, the CIE (“Commission Internationale de l’Éclairage”) in 1931 defined three spectral as primary color stimuli – red R = 700.0 nm, green G = 546.1 nm and blue B = 435.8 nm. The sensitivity of the cones, however, is also dependent on the angle of observation. Standardisation was implemented using the CIE standard observer concept. The standard observer, like the type, is a table of numerical values that represent an “average standard human observer”, so the color perceptions are not specific to an individual observer.

Luminous efficiency of the human eye – In the visible range of the (400 nm - 700 nm), the human eye perceives the same spectral radiances to have different at different wavelengths. This spectral luminous efficiency of the eye was measured and standardised by the CIE for the standard observer. The V() curve applies for all photopic vision, in which the cones in the are active. The Luminous efficiency of the eye values for the luminous efficiency for photopic vision were drawn up in 1923 by the CIE, and adopted in 1924 to carry out colorimetric calculations. 1,5 The V´() curve applies for scotopic vision, in which the rods are the active receptors. The luminous efficiency V’ V values for scotopic vision were gathered into a standard 1,0 by the CIE in 1951. In the luminous density range between photopic and scotopic vision – the mesopic range (twilight vision) – the spectral sensitivity curve shifts 0,5 with a decreasing adaptive luminous density, even for shorter wavelengths. Spectral radiated power Spectral radiated 0 400 450 500 550 600 650 700 750

Wavelength (nm)

Luminous efficiency of the eye Curve V = photopic vision/day = (CIE 1924) Curve V’ = scotopic vision/night = (CIE 1951) 01 Datacolor | Color and color measurement The human observer's perception of color stimulus Experiments with normal-sighted human observers were The entire range of color stimuli perceivable by people carried out in order to define a “standard observer” as could be recorded in this way; color vision ability was the basis for all colorimetric measures and calculations. recorded numerically. A divided screen was used in these experiments. On The most significant experiments in determining the one side, one specific color was projected, and on trichromatic perception of color stimulus of the eye were the other side were three projectors in the light colors carried out in 1928 by W. D. Wright and 1931 by J. Guild. blue, green and red. The observer had to reconstruct The trials by Wright and Guild were able to demonstrate the color impression of the first color by changing the that the numerical values differed slightly from each other lightness of the three light sources (three ). because the primary light sources were slightly different. The radiation quantity was noted in a table for each These experiments in additive corroborated change to the three primary light sources and each Young's three-component theory. change to the experimental light at each wavelength.

1,4 Red 1,2 1,0 Green 0,8 0,6 0,4 Blue Experiment in the 0,2 Versuch der additiven Mischung von additive mixing of partition Lichtstrahlung 0 light radiation -0,2 Observer

Light intensity Light -0,4

-0,6 R G B projection surfaceWhite -0,8 Test lamp Screen -1,0 400 450 500 550 600 650 700

Wavelength (nm)

Chapter 09 | Color measurement – the CIE 1931 system 02 Chapter 9 The colorimetric 2° or small field CIE31 standard observer In the experiments on mixing, it was shown On account of these restrictions, in 1931, the CIE that not all real colors could be generated with the defined three arbitrary imaginary measurement values (X, CIE's three RGB primary color stimuli. It was sometimes Y and Z) as primary color stimuli – selected from the point necessary to mix the color sample with one of the three of view of easy colorimetric evaluation. All real colors primary colors to reach equivalence with the mixture from can be represented by additive mixing using these three the two remaining primary colors. This means that certain measurement values. These measurement values are colors can only be mixed from the three primary colors called ‘CIE standard tristimulus values’, and the color if one primary color contributes a “ portion”. For space is called ‘CIE XYZ color space’. some spectral colors, therefore, the colorimetric values Transformation of the RGB primary color stimuli into must be negative. the XYZ primary color stimuli was carried out with the following characteristics:

„„ Negative values in the equations were to be eliminated (negative values were extremely difficult to process ≠ G1+G2 electronically at that time) „„ Definition of a new system with three ‘imaginary’ G1 G2 G3 primary color stimuli x, y, z, so the spectral locus falls 0 into a triangle that is defined by these three primary color stimuli „„ The function y was selected and calculated to correspond with the luminous efficiency function V ( ) (CIE 1924), therefore simplifying the calculations „„ The function z was equated with zero for most of the visible spectral range, also to simplify the calculations P P+G3 = G1+G2 „„ The calculations were carried out for a light source with equal radiation as well as for the entire spectral range, G3 G1 G2 G3 so the areas of the x, y, z-functions are the same. 0 The resulting functions are called CIE-x, y, z-color-matching functions. They are not real functions in the proper sense; they represent the average standard observer.

P P = G1+G2-G3

G1 G2 G3

0 z Negative primary color portion in color 2,0 matching by mixing the primary color with the color sample P. 1,5 y x

1,0

P + G3 = G1+ G2 density factorLuminous 0,5 is equivalent to 450 500 550 600 650 700

P = G1+ G2 - G3 0 400 Wavelength (nm) P ... Color sample, G1, G2, G3 ... three primary colors

Color-matching functions x, y, z of the 2° standard observer (CIE31)

03 Datacolor | Color and color measurement The colorimetric 10° or large field CIE64 The field of vision of 2 ° standard standard observer observer corresponds to the size of a coin of 1 Euro that you hold with To allow human perception to be incorporated in a an outstretched arm in front of you. controlled way into a measurement result, it was necessary to define a standard for human vision. This standardised vision was defined by the CIE standard observers. The CIE31 standard observer or 2° standard observer is traced back to an experiment to determine the average color perception of the human observer, For this, it was 2° considered that humans perceive colors most precisely when they encounter the area in the eye where vision is sharpest (fovea, spot). With a normal viewing distance from a color sample, this region deviates by about 2° from the optical axis of the eye. From this, it was determined that the angle at which the standard observer sees should be exactly 2°. This corresponds to a field of vision the size of a 1 euro coin that you hold in front of you with your arm outstretched. The normal field of vision of human perception, however, is greater than this 2° area. Jacobsen (1948) and Judd (1949) were also able to demonstrate that the colorimetric calculations based on the 2° angle did not correspond very well to the actual observations in the range of the short wavelengths (especially for ). As a result, the CIE proposed another standard observation angle in 1960 10° – the 10° standard observer. This corresponds to a field of vision the size of an A4 page at a standard viewing distance of 30 cm. The color-matching functions x10, y10, z10 of this new standard observer were then ultimately specified by the CIE as standard in 1964.

CIE 1931 2° standard observer CIE 1964 10° standard observer 2,0 x y z Color-matching functions z 10° 1,5

y 2° 1,0 x

0,5 Spectral radiated power Spectral radiated

0 400 450 500 550 600 650 The field of vision of 10 ° standard observer is Wavelength (nm) 700 about 27 times as large as the 2 ° standard observer.

Color-matching functions x, y, z of the 10° standard observer (CIE 1964)

Chapter 09 | Color measurement – the CIE 1931 system 04 Chapter 9 The diagram according to the Example: Calculation of the standard tristimulus CIE standard colorimetric system CIE31 value X of a color specification. For each wavelength of the visible spectral range, the Using the standard color-matching functions x, y, z of the value of the color-matching function x is multiplied by standard observer, the spectral curve can be converted the value of the spectral radiated power S of a standard into 3 values – the standard tristimulus values X, Y and Z. illuminant type for the same wavelength. This By means of these standard tristimulus values, the color calculation is carried out for each selected wavelength of an object or a light source can be determined with increment (Δλ) in the entire spectral range (400 nm – 700 three measurement values. nm). The total of these calculated products for all wavelengths (∑ of 400 – 700 nm) is then calculated.

x x

= Color perception

x x

= colorimetric description

700 = ∑ x X 400 x

= ∑ 700 x Y 400 x

700 = ∑ x Z 400 x

05 Datacolor | Color and color measurement For the precise classification of color, we need: Therefore, the mathematical formula for the standard tristimulus value X of the colored object is: 1. The radiation distribution for the illuminant type (E) 2. The wavelength-dependent physical reflectance/ reflection coefficient of the object (R) 700 X = ∑ E () • R () • x () •  3. The color specifications for the observer/the color- 400 matching function of the standard observer x

For the calculation of the color specification of a colored where object, the radiation S () is equated with the product E () dE = the radiation of the light source • R () for each wavelength, that is, the radiation of the (illuminant type) light source E (), which illuminates an object, is reduced R = the reflection coefficient of the object by the percentage of the reflection coefficient of this object, x = the color-matching function of the standard and this is the case for each wavelength increment ( ). observer  = symbol for the wavelength; if () comes after another symbol, this means that it is wavelength-dependent

Y and Z are calculated in the same way.

250 Light source ( E ) Object ( R )

200 100

150 75

100 50

50 25

0 400 450 500 550 600 650 700 0 400 450 500 550 600 650 700

Standard illuminant type CIE D65 – spectral radiated power Red sample – reflection curve

Observer ( x y z ) Results

2,0 z X = = 33.16 1,5

y Y = = 20.89 1,0 x

0,5 Z = = 12.71

0 400 450 500 550 600 650 700

2° CIE31 standard observer – color-matching functions CIE color specifications X – Y –Z = 3 numerical values

Spectral radiated power (E) x reflection coefficients (R) x color-matching functions (x,y,z) =3 color values (X,Y,Z)

The calculation principle for the standard color values XYZ

Chapter 09 | Color measurement – the CIE 1931 system 06 Chapter 9

The chromaticity diagram according to the CIE standard colorimetric system CIE31 In order to be able to more clearly represent the three- dimensional color space perceived by the observer (according to chromaticity), the two-dimensional CIE Using the standard tristimulus values XYZ of the CIE31 standard chromaticity diagram was developed. This can be standard colorimetric system, a color can be determined used to determine the color specifications separately from with high precision. However, correlation with the visual the lightness. The CIE introduced the standard chromaticity evaluation is unfortunately often very difficult. Even if the coordinates x, y, z for this, whereby x and y are used to standard tristimulus value Y corresponds relatively well to determine the chromaticity. “Small x” is the relatively red the sense of luminance, the X and Z values can only with coordinate and, accordingly, “small y” is the relatively great difficulty be approximated to the criteria for and green coordinate (z being unnecessary, since z =1-x-y). chroma in the of colors. For the shoe in our example, the chromaticity coordinates appear as follows: x = 0.4967 and y = 0.3129 for standard and a 2° standard observer. y 520

0,8 540

0,7 560 500 0,6

580 0,5

600 0,4 Coordinates of the color shade of the red chair in the CIE

0,3 700 0,2 480 X 0,1 x = X +Y+Z 460 400 Y 0,1 0,2 0,3 0,4 0,5 0,6 0,7 x y = X +Y+Z

Z z = X+Y+Z 07 For graphical representation, the CIE proposed a Conclusion – notes coordinate system, with x as the abscissa and y as the ordinate. The chromaticity coordinates of the pure colors in the visible spectral range form a concave curve shaped In summary, so far it can be said that the color of an object, like the “sole of a shoe”. This is called the spectral locus. such as the red sample, can be precisely determined In the inner area of the “sole of the shoe”, also called using the CIE31 standard colorimetric system, by means the color triangle, all possible colors are represented (in of the three measurement values X, Y and Z, and taking light). Each color point within this area has a different into account the standard illuminant type and the CIE31 chromaticity. The green and blue shades are in the upper standard observer. area of the color triangle, the violet shades on the lower The CIE31 standard colorimetric system forms the left-hand side, and the red shades on the lower right. The scientific basis of modern color measurement. straight connection line between violet and red is called the line of ( is not a spectral color!). The All works and research on the development of new area enclosed contains the color points of all of the real colorimetric formulae from 1936 up until today have been . based on this system, and although it allowed the high precision determination of a color by means of the three In the centre of this area is the neutral achromatic point measurement values, it has repeatedly been the subject of (x=0.333, y=0.333) of a light source with equal-energy numerous studies and improvements. You can learn about radiation, also called the point. The some of these in the following chapters. changes according to the illuminant type used, as each illuminant type has a different spectral composition. Standard illuminant A (light from a lightbulb) is in an area much more yellow/ than the other standard illuminants. Standard illuminant D65 (daylight) is whiter and is close to the central area. For simpler determination and classification of a color in the CIE31 standard chromaticity diagram, the equal-hue wavelength and the chroma of a color can be defined instead of the standard chromaticity coordinates. This method allows a color to be defined according to hue and chroma, as in visual classification. This is also the advantage of this method. The equal-hue wavelength is the wavelength that corresponds to the additive color mixing for the required color. It describes the hue of the pure color point. The chroma is the percentage proportion of the pure color in the mixture. The highest chroma is equal to 1. This corresponds to the pure color. A chroma of 0 corresponds to the color of the illuminant type (white light). The chroma is at its highest on the spectral locus and its lowest at the central achromatic point.

Chapter 09 | Color measurement – the CIE 1931 system 08 Chapter 10 The color spaces

General The CIE31 standard colorimetric system, on the other hand, is based on the physical characteristics of light. The Tristimulus notation made possible the first map of color CIE system aims to achieve uniformity and standardisation space, the CIE Chromaticity Diagram. Developing a map of the light colors and sources as well as the body was a decisive moment in the science of . colors. The perceptual uniformity of the color scale is When you can locate objects on a map, you can measure not considered here. MacAdam was able to demonstrate the distance between them. this non-uniformity of the CIE31 color space with his experiments on the visual perception of colors (1942). These distances represent (however imperfectly) the color With illumination conditions constant, an observer viewed differences between the samples. The CIE Chromaticity 2 colors – one color was fixed, and the second color had Diagram was the first tool widely used to express visual to be adjusted by the observer so that it was identical to the differences using numbers. test color. This experiment was carried out with 25 different It remains the basis for the ongoing efforts to develop test colors from the CIE31 diagram. The adjusted colors and refine the maps of color space and colorimetric all lay in an ellipse around the original test colors, whereby calculations. the form and orientation of the ellipses were very different, depending on color. Today we use numbers to specify colors, describe color differences, set color tolerances and evaluate the consistency and acceptability of colored products. Most notably we now see better agreement between the numerical description of color differences and what we see visually. David L. MacAdam

History – development from 1905 to 1976

At the beginning of the 20th century, Albert Henry Munsell developed a color system on a scientific basis. He determined colors according to the measurable characteristics of color shade, lightness, and chroma, arranging them three-dimensionally. In 1905, he published “A color Notation”, which describes the system. The first color atlas showing the three-dimensional color space from different perspectives appeared in 1915. The MUNSELL color atlas was oriented to the human observer's sense of color, featuring „„ An optically balanced design (uniform color space) and „„ A method for the reciprocal determination of colors, where each color can take up only one single place.

CIE color diagram with MacAdam-Ellipsen

09 Datacolor | Color and color measurement The CIELab color space – definitions and characteristics

This prompted the CIE to develop mathematical The 1976 CIE color space, also called CIELAB color transformations for the CIE31 color space, in order to space, is based on a nonlinear transformation of the 1931 maintain a uniform color space. CIE tristimulus coordinates X, Y, Z. The development of this color space had two objectives: The CIE recommended two new systems in 1976 – the CIELuv and CIELab color spaces. To make a distinction „„ Uniformity. The calculated distances between samples from other systems (especially the Hunter system), a * was must uniformly correlate to visual differences between added to all of the parameters used (for example, L*, a*, samples b*). „„ . It should offer a simple means for the user to interpret the data. The CIELuv system is preferably used for additive color mixing, e.g. light color measurement in scanners and monitors. The CIELab system is limited to the examination The CIELab color space, with some conditions, is a of body colors. uniform scale and device-independent. Each perceivable color in color space is defined with the color point that As the CIELab system is the most commonly used in color has coordinates {L*, a*, b*}. Here, in application of the measurement applications, we will examine this system opponent color theory, green and red lie against the a* more closely. axis. The b* axis corresponds to the opponent colors blue and yellow. The L* axis stands perpendicular on this plane and represents the lightness. The L* axis can also be referred to as the neutral axis, as its endpoints are black (L=0) and white (L=100), the values in between on this axis are achromatic shades of grey.

The CIELab color space: the determination methods.

L* = 100

+ b*

– a* + a*

- b*

L* = 0

Chapter 10 | The color spaces 10 Chapter 10 The formula for the transformation and calculation of the CIE76 (CIELab) color space based on XYZ (CIE31) is as follows::

Color values: : L* a* b*

3 Y Y X Y L* = 116 – 16 for > 0.008856 a* = 500 [ f ( ) – f ( ) ] Yn Yn Xn Yn

Y Y Y Z L* = 903.3 ( ) for ≤ 0.008856 b* = 200 [ f ( ) – f ( ) ] Yn Yn Yn Zn

where

3 X X X X X „ If > 0.008856 , f ( ) = , else f ( ) = 7.787 ( ) Xn Xn Xn Xn Xn

3 Y Y Y Y Y „ If > 0.008856 , f ( ) = , else f ( ) = 7.787 ( ) Yn Yn Yn Yn Yn

3 Z Z Z Z Z „ If > 0.008856 , f ( ) = , else f ( ) = 7.787 ( ) Zn Zn Zn Zn Zn

The values Xn, Yn, Zn are the color values of the absolute white (ideally an achromatic color stimulus) of a body

color for the particular CIE standard illuminant type (e.g. D65 or A). Under these conditions, Xn, Yn, Zn are color

values for the standard illuminant type, where Yn is equal to 100.

„ Lightness CIE76: L* The parameter L* is defined by the following relation:

3 Y Y E.g. for D65/10°: L* = 116 – 16 for > 0.008856 Yn Yn X = 94.81 n Y Y L* = 903.3 ( ) ≤ 0.008856 Yn = 100.00 for Yn Yn Zn = 107.304. „ Chroma – Colourfullness CIE76: C* The parameter C* is defined by the following relation: To describe the color distances using the correlation factors of lightness, C* = (a*² + b*²) (chroma) and hue, the following defined rules „ Hue angle CIE76: h can be used: The parameter h is defined by the following relation: b* h = arc tg ( ) a*

11 Datacolor | Color and color measurement + b*

– a* + a* 1 Point 1 for standard illuminant A and 2° standard observer

2 Point 2 for standard illuminant D65 and 10° standard observer Furthermore, the CIELab color space has + b* – b* the characteristics of an Euclidean space. Each point can be described by: 100

90

„„ its perpendicularly plotted 80 coordinates L*, a* and b*, where X Y 70 a* = 500 [ f ( ) – f ( ) ] „„ L* represents the lightness Xn Yn „„ a* represents the red/green 60

color specification 50 Y Z „„ b* represents the yellow/blue b* = 200 [ f ( ) – f ( ) ] 40 Y Z color specification n n b* =34.07 1 1 30

20 b*2=19.29 2 10 Position of the color points in perpendicularly plotted coordinates – a* + a* L*, a* and b* of the CIELab system 0 10 20 30 40 50 60 70 80 90 100

– b* a*2=51.72 a*1=57.15

+ b*

– a* + a* 1 Point 1 for standard illuminant A and 2° standard „„ Or by its cylindrically plotted observer coordinates L*, C* and h, where 2 Point 2 for standard illuminant D65 and 10° standard observer + b* „„ L* still represents the lightness – b* „„ C* represents the colorfulness 100 80° or the chroma 70° „„ h represents the hue angle or 90 60° the shade of the color. h* 80 50°

70 C* 40° 60 h1=30.81°

50 30°

h =20.45° 40 2 1 20° 30

20 2 10°

Position of the color points in 10 cylindrically plotted coordinates L*, C* and h of the CIELab system – a* + a* 0 10 20 30 40 50 60 70 80 90 100

C* =66.53 – b* C*2=55.20 1

As a result of the transformation, there is no chromaticity diagram for the CIELab color space. In the color planes defined by the values a*, b* or C*, h, the colors cannot be added any more. The CIELab color space is roughly (not absolutely) structured according to perception; statistically, it corresponds to human visual color perception. Therefore, it is not strictly uniform for color evaluation in terms of the psychology of perception, but it simplifies the interpretation of a color point and of colorimetric deviations.

Chapter 10 | The color spaces 12 Chapter 10 From color to color measurement

The previous chapters dealt with the development of color measurement, from visual evaluation to the determination of a color by means of the standardised color systems CIE31 and CIELab 1976, and always considering individual or isolated colors. The following chapters will deal with the evaluation of distances between two or more colors and the acceptability of colors.

y

VISIBLE SPECTRUM 0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

400 nm 500 nm 600 nm 700 nm 0,1 0,2 0,3 0,4 0,5 0,6 0,7 x

Prior to Color measurement With Color measurement Always 1905-1915 1931 1976

Language Munsell-Atlas CIE31 Color triangle CIELab color space

"red" Sample X = 33.16 x = 0.4967 L* = 52.15 L* = 52.15 "vibrant" 2.5 R 5/12 Y = 20.89 y = 0.3129 a* = +51.72 C* = 55.20

"light" Z = 12.71 Dominant L1 = 628 nm b* = +19.29 h = 20.45° for D65 / 2° Luminous density = 46.9 % for D65 / 10° for D65 / 10° for D65 / 2°

Limited Determination that can Determination via perpendicularly Determination via cylindrically First calculation First objective determination vocabulary be compared plotted coordinates plotted coordinates

Determined by people Colorimetric calculation

SUBJECTIVE OBJECTIVE

13 Datacolor | Color and color measurement From color … to color measurement From technical language … to the 1931 CIE color space … and to the 1976 CIELab color space From the subject … via the object to the measurement

Prior to Color measurement With Color measurement Always 1905-1915 1931 1976

Language Munsell-Atlas CIE31 Color triangle CIELab color space

"red" Sample X = 33.16 x = 0.4967 L* = 52.15 L* = 52.15 "vibrant" 2.5 R 5/12 Y = 20.89 y = 0.3129 a* = +51.72 C* = 55.20

"light" Z = 12.71 Dominant L1 = 628 nm b* = +19.29 h = 20.45° for D65 / 2° Luminous density = 46.9 % for D65 / 10° for D65 / 10° for D65 / 2°

Limited Determination that can Determination via perpendicularly Determination via cylindrically First calculation First objective determination vocabulary be compared plotted coordinates plotted coordinates

Determined by people Colorimetric calculation

SUBJECTIVE OBJECTIVE

Chapter 10 | The color spaces 14 • • •

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October, 2019